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lina2011 [118]
3 years ago
6

8 (Picture) CONVERGENT AND DIVERGENT SERIES PLEASE HELP!!

Mathematics
1 answer:
djverab [1.8K]3 years ago
7 0

Answer:

<em>The correct answer choice is:   B</em>

Step-by-step explanation:

<u>Culture A</u>

Initial number of cells = 1000

The number of cells is raised by 200 each day and every day thereafter.

So, the number of cells raised in one month(30 days) =200\times 30=6000

Thus, the total number of cells in culture A at the end of one month will be:  1000+6000=7000

<u>Culture B</u>

Initial number of cells = 1000

The number of cells is increased by 8% each day and every day thereafter.

<em>Formula for exponential growth is:</em>   A=P(1+r)^t, where P= Initial amount, A= Final amount, r= Rate of growth in decimal form and t= Time duration.

Using the above formula, the number of cells after 30 days will be.....

A= 1000(1+0.08)^3^0\\ \\ A=1000(1.08)^3^0= 10062.656...


That means, Culture B is more effective in promoting cell growth.

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During optimal conditions, the rate of change of the population of a certain organism is proportional to the population at time
Lana71 [14]

Answer:

The population is of 500 after 10.22 hours.

Step-by-step explanation:

The rate of change of the population of a certain organism is proportional to the population at time t, in hours.

This means that the population can be modeled by the following differential equation:

\frac{dP}{dt} = Pr

In which r is the growth rate.

Solving by separation of variables, then integrating both sides, we have that:

\frac{dP}{P} = r dt

\int \frac{dP}{P} = \int r dt

\ln{P} = rt + K

Applying the exponential to both sides:

P(t) = Ke^{rt}

In which K is the initial population.

At time t = 0 hours, the population is 300.

This means that K = 300. So

P(t) = 300e^{rt}

At time t = 24 hours, the population is 1000.

This means that P(24) = 1000. We use this to find the growth rate. So

P(t) = 300e^{rt}

1000 = 300e^{24r}

e^{24r} = \frac{1000}{300}

e^{24r} = \frac{10}{3}

\ln{e^{24r}} = \ln{\frac{10}{3}}

24r = \ln{\frac{10}{3}}

r = \frac{\ln{\frac{10}{3}}}{24}

r = 0.05

So

P(t) = 300e^{0.05t}

At what time t is the population 500?

This is t for which P(t) = 500. So

P(t) = 300e^{0.05t}

500 = 300e^{0.05t}

e^{0.05t} = \frac{500}{300}

e^{0.05t} = \frac{5}{3}

\ln{e^{0.05t}} = \ln{\frac{5}{3}}

0.05t = \ln{\frac{5}{3}}

t = \frac{\ln{\frac{5}{3}}}{0.05}

t = 10.22

The population is of 500 after 10.22 hours.

7 0
2 years ago
D 1. Given the number 47,135,280, what is the place value of the number "1"?
Anit [1.1K]

Answer:

one Hundred Thousand

Step-by-step explanation:

4 0
3 years ago
A restaurant uses 290 pounds of onions every 2 and a half weeks. If they continue to use onions at the same rate, how many pound
Archy [21]
290/2.5 = 116 pounds per week

116 * 6 = 696 pounds
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2 years ago
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Find the missing side of the triangle. Round your answer to the nearest tenth if necessary.
Soloha48 [4]

Answer:

Step-by-step explanation:

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5 0
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